Particle acceleration and Alfvén wave generation by an interplanetary shock

Based on the event observed by ISEE 3 near the Earth’s orbit at 01:21 UT on April 5, 1979, we investigate the diffusive shock acceleration of ions and the generation of Alfvén waves by accelerated particles near the quasi-parallel parts of interplanetary shock fronts within a quasi-linear approach. The theory is shown to give an excessively high level of Alfvén wave generation by accelerated particles at significant deflection angles of the interplanetary magnetic field from the normal to the shock front. At the Earth’s orbit, the Alfve´ n waves produced by accelerated ions are confined within the frequency range 5 × 10^?2?0.5 Hz, and their spectral peak with a wave amplitude δB ≤ B corresponds to a frequency ν = (1?2)×10^?2 Hz. The high-frequency part of the wave spectrum (ν ≥ 0.5 Hz) is subjected to damping on thermal protons. The calculated spectra of the accelerated ions and Alfvén waves generated by them reproduce the main features observed in experiments.     

Statistical Properties of Alfvén Ion Cyclotron Waves and Kinetic Alfvén Waves in the Inner Heliosphere

Alfvén ion cyclotron waves(ACWs) and kinetic Alfvén waves(KAWs) are found to exist at <0.3 au observed by Parker Solar Probe in Alfvénic slow solar winds. To examine the statistical properties of the background parameters for ACWs and KAWs and related wave disturbances, both wave events observed by Parker Solar Probe are selected and analyzed. The results show that there are obvious differences in the background and disturbance parameters between ACWs and KAWs. ACW events have a relatively hi...     

On the origin of energetic particles in the foreshock region of the Earth’s bow shock

We consider the processes related to the formation of the so-called foreshock region upstream of the Earth’s bow shock. We suggest a model based on the surfing of pick-up ions in the bow shock front in terms of which the ion acceleration mechanism in the front can be explained. We ascertain the physical conditions under which the accelerated ions lie upstream of the shock front and determine the direction of motion of the energetic ions. We conclude that it is this population of energetic ions (longitudinal beams) that plays a major role in forming the ion foreshock boundary.     

Quantum treatment of kinetic Alfvén wave

Dispersion properties of kinetic Alfvén wave in quantum magnetoplasma are derived. The quantum contribution to the Landau damping of kinetic Alfvén wave is also derived by using linearized Vlasov equation which contains the Bohm quantum potential. Classical Landau damped kinetic Alfvén waves play an important role in turbulence of astrophysical plasmas. The quantum modification in Landau damping of kinetic Alfvén wave can also play a significant role in changing the scaling law of turbulent spectra as well as the formation of damped localized Alfvénic structures in dense astrophysical plasmas.     

Alfvén waves and the sunspot phenomenon

Parker's explanation of the sunspot phenomenon in terms of the enhanced emission of Alfvén waves (solar vulcanology) is shown to be compatible with observation only if 90% of the waves propagate downwards. Further difficulties arise if the region of cooling by Alfvén wave generation is restricted to a depth of 2 Mm. However, it is shown that, if Alfvén wave generation is included in a recent model proposed by Meyer, Schmidt, Weiss and Wilson, these difficulties may be resolved. The problem of the sharp umbra and penumbra boundaries is discussed and it is shown that features of this combined model are relevant to the flare phenomenon.     

Nonlinear interaction of inertial Alfvén wave with magnetosonic wave and cavitation phenomena

In the present paper, authors have investigated nonlinear interaction of inertial Alfvén wave with magnetosonic wave for low β-plasma (β?m _e /m _i ). Authors have developed the set of dimensionless equations in presence of ponderomotive force due to inertial Alfvén wave in the dynamics of magnetosonic wave. Stability analysis and numerical simulation have been carried out to study the effect of nonlinear coupling between waves which result in the formation of localized structures and density cavity, applicable to auroral region and solar corona. The result reveals that localized structure and density cavity becomes more complex and intense in nature in quasi steady state. From the obtained result, we found the density fluctuations ～0.1n ₀, consistent with the FAST spacecraft observation.     

A two-fluid modeling of kinetic Alfvén wave turbulence

We present an analytical model to explore the magnetic field turbulent spectrum by coupled high-frequency kinetic Alfvén wave (KAW) and slow mode of Alfvén wave (AW). The spectrum is computed as a realization of energy cascades from larger to smaller scales for a specific case of solar wind plasma at 1 AU. A two-fluid technique is implemented for the derivation of model equations leading two wave modes. These coupled, nonlinear equations are solved numerically. The nonlinearity in the system arises due to nonlinear ponderomotive force, which is believed to be responsible for the wave localization and magnetic islands formation. The numerical results show that the magnetic islands grow with time and attain a quasi-steady state after the modulation instability is saturated. The magnetic field spectrum and associated spectral indices are computed near the time of saturation of instability. The simulated spectrum in dispersion region follows a power-law with an index of ?2.5. The steeper spectrum could be attributed as energy transfer from larger to smaller scales and helps to study turbulence in solar wind. The magnetic field spectrum and spectral index show a good agreement with the observation of solar wind turbulent spectra.     

Inertial Alfvén wave induced turbulent spectra in aurora

In the present paper, we investigate the localization of weak inertial Alfvén wave (IAW) in the presence of finite amplitude magnetosonic fluctuations in low β plasmas (β?m _e /m _i ). When IAW is perturbed by these fluctuations, localized structures of IAW magnetic field intensity are formed. We have developed a semi analytical model based on paraxial approximation to study this interaction. Numerical method has also been used to analyse the localized structures and magnetic fluctuation spectrum of IAW. From the obtained results, we find that the magnetic turbulent spectrum upto k _x λ _e ≈3 fits power law spectrum with an index consistent with the Kolmogorov $k_{x}^{ - 5/3}$ law, here λ _e is the electron inertial length. Furthermore, at shorter wavelengths the spectrum steepens to about $k_{x}^{ - 3.8}$ . Energy transfer from larger lengthscales to smaller lengthscales through this mechanism may be responsible for the observed parallel electron heating in auroral region. Results obtained from the simulation are consistent with the observations recorded from various spacecrafts like FAST, Hawkeye and Hoes 2.     

Coherent structures and spectral shapes of kinetic Alfvén wave turbulence in solar wind at 1 AU

This paper presents the generation of kinetic Alfv én wave(KAW) coherent structures of magnetic filaments applicable to solar wind at 1 AU, when the background plasma density is modified by parallel ponderomotive force and Joule heating. The inhomogeneity in the magnetic field, which was included as a perturbation in the transverse direction of the magnetic field, takes energy from the main pump KAWs and generates the filamentary structures. When the intensity is high enough, the filaments are broken down and the energy initially confined to low wavenumbers is redistributed to higher wavenumbers, leading to cascades of energy at small scales less than the ion acoustic gyroradius or comparable to electron gyroradius.The magnetic field spectral profile is generated from the numerical simulation results, and its dependence on different directions of the wavevector and initial conditions of the simulation representing the transverse magnetic field inhomogeneity is studied. The relevance of these results with other spacecraft observations and measurements is also pointed out.     

Alfvén Reflection and Reverberation in the Solar Atmosphere

Magneto-atmospheres with Alfvén speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A?common example involves a uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfvén speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfvén waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as $\mathcal{O}(t^{-1})$ or $\mathcal{O}(t^{-1}\ln t)$ , depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfvén waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.     

Nonlinear kinetic Alfvén wave with Poisson equation correction in the low aurora

Nonlinear kinetic Alfvén waves where m _e /m _i , have been solved both with and without the Poisson equation correction. It is found that the ratio of the perpendicular electric field and magnetic field, and the ratio of parallel and perpendicular electric field increase with deepening of the depressive density soliton. The former ratio may be larger than the Alfvén velocity in the case of a large amplitude solitary kinetic Alfvén wave. The Poisson equation correction is important for the nonlinear kinetic Alfvén wave propagating along the magnetic field, which solves a puzzle of Sagdeev potential to approach infinity in the limit ofK _x 0. This correction causes the solitary KAW possessing an electrostatic character along the direction of wave moving frame. These results have been compared with the observations from the Freja satellite in the low aurora.     

Numerical simulations to study kinetic Alfvén wave and whistler wave spectra in solar wind plasma

The numerical simulations of the model equation governing the nonlinear evolution of kinetic Alfvén wave (KAW) in solar wind plasmas are performed. The nonlinear dynamical equation of KAW satisfies the modified nonlinear Schrödinger MNLS equation when the ponderomotive nonlinearity is incorporated in the KAW dynamics. The effect of Landau damping is taken into account in the KAW dynamics. The coherent (in the absence of Landau damping) and damped (with Landau damping) localized structures of pump KAW as a consequence of ponderomotive nonlinearity have been studied in the solar wind at 1 AU. A weak whistler signal propagating in these localized structures is amplified which leads to the development of its own coherent and damped localized structures. Magnetic field (KAW) and electric field (whistler wave) power spectra and their spectral indices are calculated. Our results reveal the change in spectral index because of the damping effect which has good agreement with the observations. These damped structures and steeper spectra may be one of the reasons responsible for the plasma heating and particles acceleration in solar wind.     

Effect of linear waves on kinetic Alfvén wave localization and turbulent spectrum

We have presented the localization of kinetic Alfvén wave (KAW) in intermediate β plasma (m _e /m _i ?β?1) by developing a model based on pump kinetic Alfvén wave and finite amplitude magnetosonic fluctuations. When KAW is perturbed by these background magnetosonic fluctuations, filamentary structures of KAW magnetic field are formed. First, a semi analytical model based on paraxial approximation has been developed to understand this evolution process. Localized structures and magnetic fluctuation spectrum of KAW has also been studied numerically for finite frequency of KAW. The calculated magnetic fluctuation spectrum follows two types of scalings. Above the proton gyroradius scale lengths (in inertial range), spectrum follows Kolmogorovian scaling. Below this scale dispersion starts and the spectrum steepens to about \(k_{x}^{-2.5}\) . The result shows the steepening of power spectra which can be responsible for particle acceleration in solar wind due to the energy transfer from larger to smaller lengthscales. Obtained magnetic turbulent spectra are consistent with observations of Cluster spacecraft in solar wind.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Alfvén waves in the solar atmosphere

The linearized propagation of axisymmetric twists on axisymmetric vertical flux tubes is considered. Models corresponding to both open (coronal hole) and closed (active region loops) flux tubes are examined. Principal conclusions are: Open flux tubes: (1) With some reservations, the model can account for long-period (T 1 hr) energy fluxes which are sufficient to drive solar wind streams. (2) The waves are predicted to exert ponderomotive forces on the chromosphere which are large enough to alter hydrostatic equilibrium or to drive upward flows. Spicules may be a consequence of these forces. (3) Higher frequency waves (10 s T few min) are predicted to carry energy fluxes which are adequate to heat the chromosphere and corona. Nonlinear mechanisms may provide the damping. Closed flux tubes: (1) Long-period (T 1 hr) twists do not appear to be energetically capable of providing the required heating of active regions. (2) Loop resonances are found to occur as a result of waves being stored in the corona via reflections at the transition zones. The loop resonances act much in the manner of antireflectance coatings on camera lenses, and allow large energy fluxes to enter the coronal loops. The resonances may also be able to account for the observed fact that longer coronal loops require smaller energy flux densities entering them from below. (3) The waves exert large upward and downward forces on the chromosphere and corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Nonlinear evolution of 3D-inertial Alfvén wave and turbulent spectra in Auroral region

In the present paper, we have investigated nonlinear interaction of three dimensional (3D) inertial Alfvén wave and perpendicularly propagating magnetosonic wave for low β-plasma (β?m _e /m _i ). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to 3D-inertial Alfvén wave in the dynamics of perpendicularly propagating magnetosonic wave. Stability analysis and numerical simulation has been carried out to study the effect of nonlinear coupling on the formation of localized structures and turbulent spectra, applicable to auroral region. The results reveal that the localized structures become more and more complex as the nonlinear interaction progresses. Further, we have studied the turbulent spectrum which follows spectral index (～k ^?3.57) at smaller scales. Relevance of the obtained results has been shown with the observations received by various spacecrafts like FAST, Hawkeye and Heos 2.     

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.     

Tunneling and interference of Alfvén waves

The propagation and interference of Alfvén waves in magnetic regions is studied. A multilayer approximation of the standard models of the solar atmosphere is used. In each layer, there is a linear law of temperature variation and a power law of Alfvén velocity variation. The analytical solutions of a wave equation are stitched at the layer boundaries. The low-frequency Alfvén waves (P > 1 s) are able to transfer the energy from sunspots into the corona by tunneling only. The chromosphere is not a resonance filter for the Alfvén waves. The interference and resonance of Alfvén waves are found to be important to wave propagation through the magnetic coronal arches. The transmission coefficient of Alfvén waves into the corona increases sharply on the resonance frequences. To take into account the wave absorption in the corona, a method of equivalent schemes is developed. The heating of a coronal arch by Alfvén waves is discussed.     

On one mechanism for the generation of a reverse solar wind shock in the magnetosheath in front of the Earth’s magnetosphere

A possible mechanism for the generation of a reverse fast shock in the magnetosheath in the solar wind flow around the Earth’s magnetosphere is considered. It is shown that such a shock can emerge through the breaking of a nonlinear fast magnetosonic compression wave reflected from the magnetopause toward the bow shock rear. In this case, the magnetopause is represented as a tangential discontinuity with a zero normal magnetic field component at it and the mechanism under consideration is assumed to be secondary with respect to the sudden disturbance of the bow shock-Earth’s magnetosphere system by a nonstationary solar wind shock. A possible confirmation of the process under study by in-situ SC3 experimental observations of the bow shock front motion on the Cluster spacecraft is pointed out.